Frequency conversion, or modulation, of a signal from one carrier frequency to another (where the bandwidth of the signal is much less than the carrier frequency), is an obvious and central part of any radio receiver or transmitter. In the classic linear super heterodyne receiver design, a modulated radio frequency (RF) carrier wave is frequency converted through a descending sequence of intermediate frequencies (or IF's) until the underlying modulation (sometimes referred to as the `envelope` or `baseband signal`) is centered at zero-frequency and the embedded information (whether an analog signal or modulated digital data) may be extracted. Similarly, efficient transmission and spectrum sharing requires frequency conversion of the baseband signal to an appropriate carrier frequency, although in order to simplify the following discussion the focus will be on frequency demodulation or downconversion.
Most contemporary frequency converters (or `mixer`) circuits are based on the doubly balanced mixer (DBM) or `diode-ring` design. It is well known that because of tolerances in the component diode characteristics, and stray capacitances and inductances in the component transformers, DBM's can suffer from carrier feed through (that is, local oscillator port to RF output port coupling) as well as nonlinear signal distortion in the IF to RF signal path. These problems are further complicated in the case of digital communications systems employing modulation schemes such as BPSK, QPSK, OQPSK, .pi./4-QPSK, M-ary PSK etc. In these instances, quadrature demodulation of the passband signal is generally required to recover the complex baseband signal used in transmission. In a quadrature mixer, the basic problems of the analog DBM persist, but since two local oscillator reference frequencies of equal amplitude and with a 90.degree. phase difference are now required, there is the additional problem of local oscillator amplitude and phase balancing.
The problems inherent in DBM's can be avoided by the use of discrete-time digital signal processing (DSP) techniques, and this has led to the development of a general class of devices known as numerically controlled oscillators (NCO's). An NCO typically comprises a multibit phase accumulator, single-quadrant sine function lookup table, and a complex digital multiplier. When operating as a mixer, its function is to transform a passband signal y(k) through the discrete-time complex frequency shift operator ##EQU1## to form the complex baseband signal x(k) where f.sub.c is the passband center frequency and f.sub.s is the sample rate. The NCO does this by accumulating a modulo-2.pi. phase [k.DELTA..theta.].sub.2.pi. which is used to address the sine lookup table. The resulting complex exponential term is multiplied with the passband signal sample y(k) to generate x(k). .DELTA..theta. is the phase step size which establishes the effective normalized conversion frequency f.sub.c /f.sub.s.
The use of this type of digital downconversion in digital communication receivers also allows the required number of A/D converters to be reduced from two (one for each of the in-phase and quadrature signal components that are generated by an analog quadrature mixer) to one as shown in FIG. 1. This is achieved by sampling, in an A/D converter (102), the received signal as a real-valued passband waveform (100). The digital sample stream is then converted into the quadrature components by use of an NCO (103), and low pass filtering (104). Note that the sample clock f.sub.s (101) of the A/D converter (102) is selected to satisfy the Nyquist condition that the sample rate be greater than twice the maximum frequency of the modulated carrier. An alternative and less common method which is shown in FIG. 2 is to use a Hilbert filter (201)--sometimes referred to as a "phase splitter"--before the NCO. The Hilbert filter (201) implements the digital equivalent of the continuous-time impulse response h(t)=1/.pi.t which is the same as performing a Hilbert transform on the input signal to the filter. The net response of the delay (200) and the Hilbert filter (201) shown in FIG. 2 is to produce a frequency response which is zero in the negative half-plane of the frequency domain and unity in the positive half, with the result that the passband signal is reduced to a single-sided analytic signal before downconversion by the NCO (103) to baseband. Methods for the efficient design and implementation of digital Hilbert filters are well known in the literature; for example, see Digital Communications, E. A. Lee, D. G. Messerschmitt, Kluwer Academic, 1988, USA, pp. 240.
It is also well known that the structure of the NCO may be greatly simplified by choosing the final IF frequency and sample clock such that f.sub.s =4f.sub.c. This is equivalent to centering the passband carrier frequency at 0.25 Hz normalized to the A/D sample rate, which allows the sequence ##EQU2## to be reduced to the cyclic sequence {1+j0, 0-j1, -1+j0, 0+j1, 1+j0, 0-j1, . . . }. This in turn means that the NCO can be reduced to a complex multiplier whose non-signal argument is simply the sequence {1+j0, 0-j1, -1+j0, 0+j1, 1+j0, . . . }. Since the sign of both components of this multiplicand is either unity or zero, the complex multiplication used to perform downconversion is simplified. As shown in U.S. Pat. No. 4,785,463, "Digital Global Positioning System Receiver," efficient designs have been proposed for implementing this scheme in combination with the low pass filtering operation of FIG. 1. However, efficient implementations based on the Hilbert filter approach of FIG. 2 are not shown in the prior art. Thus, a need exists for such an implementation.